The present invention relates to the field of analysis and prediction of the behavior of mechanical components. It relates to a method for determining the elasto-plastic behavior of components in accordance with the preamble of claim 1.
The components of gas turbines (rotor blades, guide vanes, liners, etc.) are generally so highly loaded that they have only a finite service life. It is necessary to predict this service life if gas turbines are to be designed safely and economically.
The load on the components is composed of forces, high thermal loads, oxidation and corrosion. The mechanical and thermal loads in many cases lead to fatigue in the components even after a few thousand load cycles. This low-cycle fatigue is reproduced in isothermic situations by LCF (low cycle fatigue) tests and in anisothermic situations by TMF (thermal mechanical fatigue) tests.
The stresses caused by the load are determined in the design phase of the gas turbine. The complexity of the geometry and/or load requires the use of the finite element (FE) method to determine the stresses. However, since necessary inelastic calculations are often not possible, generally for cost and time reasons, the service life prediction is almost exclusively based on linear-elastic stresses. Generally, only isothermal data (strain-controlled LCF tests) are available, and consequently even anisothermal cycles have to be evaluated using LCF data.
The measure used for the damage (damage law) in this case is the amplitude of the total comparative strain xcex5v,ep. If the required cycle number Nreq is to be reached in the component, the amplitude of the total comparative strain xcex5v,ep must satisfy the relationship
xcex5v,epxe2x89xa6xcex5aM(Tdam,Nreq)xe2x80x83xe2x80x83(a)
at each location of the component. xcex5aM is the permissible total strain amplitude, which is determined from isothermal LCF tests. It is to be determined for different temperatures and cycle numbers. The temperature Tdam on which the damage is based must be selected appropriately for a cycle with varying temperature.
If the decisive load acts for several minutes at high temperatures, it is necessary to reckon with additional damage. To establish the reduced service life on account of the accumulation of damage from creep fatigue and cyclic fatigue, LCF data are determined from tests with a holding time.
The extent of damage xcex5v,ep corresponds to the strain amplitude of a balanced cycle. This cycle is determined from the cycle analyzed in linear-elastic form via a modified Neuber""s rule:
"sgr"*xc2x7xcex5*="sgr"epxc2x7xcex5epxe2x80x83xe2x80x83(b)
with the vector of the linear-elastic stress amplitude "sgr"*, the vector of the elastic-plastic stress amplitude "sgr"ep, the vector of the linear-elastic strain amplitude xcex5* and the vector of the total elastic-plastic strain amplitude xcex5ep. The degree of damage xcex5v,ep is determined via a comparison hypothesis from the vector of the total elastic-plastic strain amplitude xcex5ep.
The cyclic "sgr"-xcex5 curve required to determine the total elastic-plastic strain amplitude xcex5ep is represented analytically by a modified Ramberg-Osgood model:
Then, Neuber""s rule can be used to approximately record the inelastic effects occurring in gas turbine components (blades, vanes, combustion chambers). These effects must be taken into account when predicting the service life of the structures. Hitherto, however, Neuber""s rule (b) has only been known for materials with an isotropic mechanical behavior.
Since, on account of its special properties, (anisotropic) single crystal material is increasingly being employed in gas turbine construction for the components, especially the turbine blades and vanes, it would be desirable in order to design the componentsxe2x80x94in particular with a view to determining the service life under cyclic loadsxe2x80x94to have available a calculation method which is analogous to that used for isotropic materials.
Therefore, it is an object of the invention to provide a method for the approximate determination of the elasto-plastic behavior of single crystal materials at high temperatures which can be used in particular to determine the service life of components of a gas turbine installation made from single crystal material.
The object is achieved by the combination of features described in claim 1. The essence of the invention consists in using a modified anisotropic Neuber""s rule of the form                     σ        _            *        ·                  ϵ        _            *        =                              σ          _                *            ·                                    E            _                    xe2x80x94                          -          1                    ·                        σ          _                *              =                                        σ            _                    ep                ·                                            E              _                        xe2x80x94                                -            1                          ·                              σ            _                    ep                    +                                                  σ              _                        ep                    ·                                    ∂                              σ                                  v                  ,                  ep                                2                                                    ∂                                                σ                  _                                ep                                                    ⁢                  xe2x80x83                ⁢                  α                      E            R                          ⁢                              (                                          σ                                  v                  ,                  ep                                2                                            σ                0                2                                      )                                n            -            1                              
to take account of anisotropic properties of the components as occur in particular through the use of single crystal materials.
The following relationships
"sgr"*=D{square root over ("sgr"*2)}
and
"sgr"ep=D{square root over ("sgr"ep2)}
are preferably assumed for the variables "sgr"* and "sgr"ep, where D denotes a directional vector of length 1, and the relationships "sgr"*xc2x7"sgr"*="sgr"*2 and "sgr"epxc2x7"sgr"ep="sgr"ep2 apply, and the modified Neuber""s rule in the form       σ          *      2        =            σ      ep      2        +                  σ        ep        2            ⁢                        D          _                ·                                            E              xe2x80x94                        xe2x80x94                                E            R                          ·                  D          _                    ⁢              xe2x80x83            ⁢                        σ          v                      *            2                                    σ                      *            2                              ⁢              xe2x80x83            ⁢                        α          ⁡                      (                                                            σ                  ep                  2                                                  σ                  0                  2                                            ⁢                              xe2x80x83                            ⁢                                                σ                  v                                      *                    2                                                                    σ                                      *                    2                                                                        )                                    n          -          1                    
is used, with an anisotropic correction term       D    _    ·                    E        _            _              E      R        ·      D    _  
and an inelastic correction term       σ    v          *      2                  σ      _              *      2      
According to a preferred configuration of the method, the equation according to the modified Neuber""s rule is solved using an iterative method, in particular a Newton iteration.
According to the invention, the method is used to determine the service life of gas turbine components which are under a cyclic load.